39 lines
675 B
Text
39 lines
675 B
Text
def f : nat → nat
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| 0 := 1
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| (n+1) := f n + 1
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lemma ex(a : nat) : f a ≠ 0 :=
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begin
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induction a,
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dsimp [f], intro x, contradiction,
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dsimp [f],
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change nat.succ (f a_n) ≠ 0,
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apply nat.succ_ne_zero
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end
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lemma ex2 (a : nat) : f a ≠ 0 :=
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begin [smt]
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induction a,
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{ intros, ematch_using [f] },
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{ iterate { ematch_using [f, nat.add_one, nat.succ_ne_zero] }}
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end
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lemma ex3 (a : nat) : f (a+1) = f a + 1 :=
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begin [smt]
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dsimp [f]
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end
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lemma ex4 (a : nat) : f (a+1) = f a + 1 :=
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begin [smt]
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simp [f]
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end
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lemma ex5 (a : nat) : f (a+1) = f a + 1 :=
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begin [smt]
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ematch_using [f]
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end
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lemma ex6 (a : nat) : f 0 = 1 :=
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begin [smt]
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ematch_using [f]
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end
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